91Ó°ÊÓ

• The energy delivered by the flashlight battery, $E=2.0W.h$
• Input power of the lamp,$P_{i}n=100W$
• Time of operation of the battery,$t=8.0h$
• Cost of one battery, $Cos{t}_{onebattery}=US\$0.8$
• Cost of energy, $Cos{t}_{energyunit}=US\$0.06kilowatthour$

A battery operating in a given circuit consumes some amount of energy within a given time and that is given as the power of the battery. Thus, in the given problem, a lamp is operating with the use of some batteries and consumes a desired amount of energy to stay lit up. As you know, one unit of energy consumption is considered one kilowatt per hour in a household, so using the total energy, you can get the cost rate of energy consumption by the lamp.

Formulae:

The power of a due to energy consumption,

$P=\frac{E}{t}$ ….. (i)

Where, E is the amount of energy consumed, t is the time of consumption or the battery operation of the battery.

The number of batteries in a lamp,

$N=\frac{P_{in}}{P_{out}}$ ..........(ii)

Where, P_in is the input power of the lamp and P_out is the output power delivered by the lamp.

Here, the cost of running the lap is given by the cost it takes in running the number of batteries it uses.

Now, the output power or the power delivered by one battery can be given using the given data in equation (i) as follows:

$$\begin{gathered} P_{out}=\frac{2.0W.h}{8.0h} \\ =0.25W \end{gathered}$$

Thus, the number of batteries operating for the lap is given using equation (ii) as follows:

$$\begin{gathered} N=\frac{100W}{0.25W} \\ =400batteries \end{gathered}$$

Now, the cost of operating a 100W lamp for 8.0husing batteries is given as follows:$$\begin{gathered} total\cos t=N×Cos{t}_{onebattery} \\ =400US\$0.8 \\ =\$3200 \\ =\$3.2×{10}^2 \end{gathered}$$

Hence, the required cost of the operating lamp is $3.2*10²

The total energy consumption by the lamp is given using the data in equation (i) as follows:

$\begin{array}{l}E=P.t\\ =\left(100w\left)\right(8.0h\right)\\ =800W.h\end{array}$

If one kilowatt hour energy costs US$0.06, then the cost of total energy is given as follows:

$$\begin{gathered} Total\cos t=\frac{800kW.h}{{10}^3}×US\$0.6 \\ =\$0.048 \\ =4.8cents \end{gathered}$$

Hence, the value of the required cost is 4.8cents.